Prove that the length of a curve as computed using the arc length integral does not depend
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Prove that the length of a curve as computed using the arc length integral does not depend on its parametrization. More precisely, let C be the curve traced by r(t) for a ≤ t ≤ b. Let ƒ (s) be a differentiable function such that ƒ(s) > 0 and ƒ(c) = a and ƒ(d) = b. Then r1(s) = r(ƒ(s)) parametrizes C for c ≤ s ≤ d. Verify that
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Hence By the Chain Rule we have rt tr pt S rt tr yt ...View the full answer
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